The redshift distribution of flat-spectrum radio sources with 5 GHz flux densities S _ { 5 } \gtrsim 5 mJy is a key component in using current radio lens surveys to probe the cosmological model .
We have constructed the first flat-spectrum radio sample in the flux density range 3–20 mJy .
Our new sample has 33 sources ; we have determined the redshifts of 14 of these ( 42 % complete ) .
The low mean redshift , \langle z \rangle \simeq 0.75 , of our faintest sample needs to be confirmed by further observations to improve the sample completeness .
We also increased the redshift completeness of several surveys of brighter flat-spectrum sources .
While the mean redshift , \langle z \rangle \simeq 1.1 of flat-spectrum samples fainter than 1 Jy is nearly constant , the fraction of the sources identifiable as quasars steadily drops from \sim 80 \% to \sim 10 \% as the flux density of the sources decreases .